Codes and Expansions (CodEx) Seminar
Philipp Petersen (Universität Wien)
Functions with structured singularities: completely harmless or the biggest challenge to computational math since travelling salespeople?
Functions with structured singularities appear in various areas of applied math. In image processing, they can be taken as models for natural images, they appear as solutions of transport dominated PDEs, and in classification problems where they can model the classifiers. We will review classical approaches in applied harmonic analysis which succeed or fail at approximating these functions efficiently. Then we will show how these methods can be extended to neural networks. We further study the same problem in high dimensions. In this context, we will get to know various notions of the Barron space and make a simple, yet surprising, observation about their relationship.